Chapter 15 - Worked Solutions

to selected extension questions from the OUP text Senior Physics - Concepts in Context by Walding, Rapkins and Rossiter

Q39.
Red light - 650 nm, Orange light - 580 nm, Grating - 1000 lines/cm
The spacing between the lines = 1/1000 cm = 10-5m
For the 2nd order bright fringe sin q = n l/d
For red light :
sin q = 2 x 650 x10-9/10-5 = 0.13 q = 7.47 o
For orange light :
sin q = 2 x 580 x10-9 /10-5 = 0.166, q = 6.66 o.
Q40.
A maximum occurs at l = 600 nm, A minimum occurs at l = 450 nm
n = 1.33
For light going from air to soap to air (see table 15.3) less - more - less:
destructive interference occurs at 2d = m l
constructive interference occurs at 2d = (m - ) l
therefore 2d = m x 450 nm, and 2d = (m - ) x 600 nm
therefore 450 m = 600 m - 300
m = 2
therefore 2 d = 2 x 450 nm , d = 450 nm, and 2 d = (2 - ) x 600 = 1.5 x 600
d = 450 nm, this is the wavelength in air.
lm = la / n = 450 /1.33 = 338 nm
Q41.

Destructive inference at l = 500 nm and 700 nm
For destructive inference with light going from low - medium - higher :
2 d = ( m - ) l
d = l , l , 5/4l......
for 500 nm d = 125 nm, 375 nm, 625 nm, 875 nm, ......
for 700 nm d = 175 nm, 535 nm, 875 nm, ....
the common value occurs at d = 875 nm.
But since lm = la / n, and since d = 5/4 l at 700 nm in air.
In the medium the l= 700 / 1.3 = 538.5 nm
then the thickness = 5/4 x 538.5 nm = 673 nm.
Check for l= 500
lm = 500/ 1.3 = 384.6 nm
d = 7/4 l = 7/4 x 384.6 nm = 673 nm.
Q 42.

from table 15.4 L- M - L : 2d = ( m - ) l
that is : 1 x 10-6 m = l, 3/2l, 3/2l.......
that is : l = 2 x 10-6 m , 6.7 x 10-7 m, 4 x 10-7 m, 2.86 x 10-7 m ...
this is the thickness in the medium. In air l = lm x n
= 2.9 x 10-6m , 9.7 x 10-7m, 5.8 x 10-7 m, 4.14 x 10-7 m...
= 2900 nm, 970 nm, 580 nm, 414 nm....
from table 15.4 Indigo- violet 400 - 420 nm
and green light goes from 490 - 580 nm
therefore you will see Indigo-violet, and green light.
Q43.

At the apex destructive interference occurs. The first constructive interference line occurs at l of air gap between the slides. Then at 3/4l , 5/4l......
Since the paper is 5 cm from the end and the bands are 0.4 mm apart then there are 50 /0.4 or 125 gaps.
Therefore the edge of the paper is over the 124th bright band.
Since 2d = (m - ) l
2d = (124 - ) x 650 x 10-7m
d = 4 x 10-5m
Q44.
Example of answer:
1. Coat a glass slide with black paint.
2. Put 2 razor blades together and scratch them across the slide
3. Use a laser and double slit interference to measure the distance between the slits, that is the thickness of a single razor blade.
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